Similitude theory allows engineers, through a set of tools known as similitude methods, to establish the necessary conditions to design a scaled (up or down) model of a full-scale prototype structure. In recent years, to overcome the obstacles associated with full-scale testing, such as cost and setup, research on similitude methods has grown and their application has expanded into many branches of engineering. The aim of this paper is to provide as comprehensive a review as possible about similitude methods applied to structural engineering and their limitations due to size effects, rate sensitivity phenomena, etc. After a brief historical introduction and a more in-depth analysis of the main methods, the paper focuses on similitude applications classified, first, by test article, then by engineering fields.

The scope of this work is to consolidate research dealing with the vibroacoustics of periodic media. This investigation aims at developing and validating tools for the design and characterization of global vibroacoustic treatments based on foam cores with embedded periodic patterns, which allow passive control of acoustic paths in layered concepts. Firstly, a numerical test campaign is carried out by considering some perfectly rigid inclusions in a 3D-modeled porous structure; this causes the excitation of additional acoustic modes due to the periodic nature of the meta-core itself. Then, through the use of the Delany–Bazley–Miki equivalent fluid model, some design guidelines are provided in order to predict several possible sets of characteristic parameters (that is unit cell dimension and foam airflow resistivity) that, constrained by the imposition of the total thickness of the acoustic package, may satisfy the target functions (namely, the frequency at which the first Transmission Loss (TL) peak appears, together with its amplitude). Furthermore, when the Johnson–Champoux–Allard model is considered, a characterization task is performed, since the meta-material description is used in order to determine its response in terms of resonance frequency and the TL increase at such a frequency. Results are obtained through the implementation of machine learning algorithms, which may constitute a good basis in order to perform preliminary design considerations that could be interesting for further generalizations.

Innovative meta-materials offer great flexibility for manipulating sound waves and assure unprecedented functionality in the context of acoustic applications. Indeed, they can exhibit extraordinary properties, such as broadband low-frequency absorption, excellent sound insulation, or enhanced sound transmission. These amazing properties have drawn the eye of the transport industry, especially for aeronautic applications where objects like these can be combined and coupled with primary structures aiming to reduce exterior and interior noise without increasing weight. However, the design of acoustic meta-materials with exciting functionality still represents a challenge, therefore there is a huge interest about the conceptualization and design of innovative acoustic solutions making use of meta-material resonance effects. The main target of the present research work is to obtain an accurate prediction of the tuning frequency of a Helmholtz-resonating device, whose resonance properties are exploited in a wide part of acoustic meta-material design. In this context, an investigation on a correction factor for the classical formulation used to estimate the Helmholtz resonance frequency starting from its geometric characteristics, accounting for different-shaped resonators with varying neck/cavity ratios, is performed. More specifically, a set of numerical simulations for several geometric configuration is considered in order to demonstrate the limits of pre-existing formulas, and a new correction factor formula is developed after theoretical considerations where it is possible. In the end, results in terms of correction factors are provided in both graphical and semi-analytical form, compared with Finite Element data.

Aluminium Foam Sandwich (AFS) panels are a type of structural configuration in which two aluminium thin layers enclose a core made of foamed aluminium. Both the metallic characteristic of the matrix and the foam porosity lead to a remarkable combination of properties which range from high specific stiffness to thermal and acoustic isolation. However, these characteristics, depending on core properties as foam density, pores morphology, type and size of gas bubbles, are obtained by means of a manufacturing process that is not fully controlled. Thus, in order to reduce the financial and temporal costs of the campaign of experimental tests needed for completely understanding the properties and potentialities of AFS panels, similitude methods can be used so that scaled-down models can be tested in place of the full-scale structure. In this work, the similitude conditions and scaling laws of Alulight® AFS panels with two different boundary conditions (simply supported and free-free) are derived and validated. In particular, two different sets of conditions are derived: the first by expliciting all the geometrical and material properties, the second by combining some parameters into just one with physical meaning, the bending stiffness. The analysis in similitude is addressed towards the prediction of vibroacoustic properties such as natural frequencies, Frequency Response Function (FRF) and radiated acoustic power. Both models in complete and partial similitude are investigated. While the former allow to reconstruct the vibroacoustic characteristics of the prototype, the latter does not. Furthermore, it is proved that it is possible to derive a simplified set of similitude conditions if many parameters are gathered into just one parameter with physical meaning.